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Two identical conducting spheres ( of negligible radius) I having charge of of opposite sign, I attract each other with a force of 0.108 N when separated by 0.5 meter. The sphere are connected by a conducting wire which is then removed when charge stops flowing and thereafter repel each other with a force of 0.036 N keeping the distance same. I What were the initial charges on the sphere?
Verified Answer
Two identical conducting spheres ( of negligible radius) I having char...
F1 = 0.108 N
r = 0.5 m
F2 = 0.036 N
Let charges on the spheres be q1 and q2 respectively.
Charges after connection gets redistributed in the spheres, so be q in each of the spheres
From conservation of charge
q1 + q2 = 2q ---1.
Again
F1 = k q1q2/r^2 ---2
F2 = k q^2/r^2 ----3
=> 0.036 = 9 x 10^9 x q^2/(0.5)^2
=> q^2 = 0.036 x (0.5)^2/9 x 10^9
=> q^2 = 0.036/(4 x 9 x 10^9)
=> q^2 = 1 x 10^-12
=> q = 1 x 10^-6 C ---4
From 2 and 3
F1/F2 = q1q2/q^2
=> 3 = q1q2/q^2
=> 3q^2 = q1q2
=> q1q2 = 3q^2
Again,
(q1 – q2)^2 = (q1 + q2)^2 – 4q1q2
= (2q)^2 – 3q^2/r^2
= q^2/ r^2
By 4
(q1 – q2) = q/r
= 1 x 10^-6/ 0.5
= 2 x 10^-6 ---5
From 1 and 4.
q1 + q2 = 4 x 10^-6 ---6.
Adding 5 and 6
q1 = 3 x 10^-6
= 3μC
Subtracting 5 from 6
q2 = 1 x 10^-6
= 1μC
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Most Upvoted Answer
Two identical conducting spheres ( of negligible radius) I having char...
Initial Attraction:
Given:
Force of attraction, F = 0.108 N
Distance between the spheres, d = 0.5 m
We can use Coulomb's law to find the initial charges on the spheres.
Coulomb's law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Mathematically, it can be expressed as:
F = k * (q1 * q2) / r^2
Where:
F is the force between the charges,
k is the electrostatic constant (9 x 10^9 Nm^2/C^2),
q1 and q2 are the charges on the spheres,
r is the distance between the spheres.
Calculating the Initial Charges:
Let the charge on one sphere be q and the charge on the other sphere be -q (opposite signs).
Using the given information, we can write the equation for the force of attraction:
0.108 = (9 x 10^9) * (q * (-q)) / (0.5)^2
0.108 = (9 x 10^9) * (q^2) / 0.25
Simplifying the equation:
0.108 * 0.25 = (9 x 10^9) * (q^2)
0.027 = (9 x 10^9) * (q^2)
q^2 = 0.027 / (9 x 10^9)
q^2 = 3 x 10^(-12)
Taking the square root of both sides:
q = ± √(3 x 10^(-12))
q = ± 1.73 x 10^(-6)
Since the spheres have opposite charges, we can assign one sphere with a charge of +1.73 x 10^(-6) C and the other with a charge of -1.73 x 10^(-6) C.
Repulsion after Removing the Wire:
After connecting the spheres with a conducting wire and then removing it, the charges on the spheres redistribute. The excess charge flows from one sphere to the other until both spheres have the same potential.
Once the charges redistribute, the spheres repel each other with a force of 0.036 N, with the distance between them still being 0.5 m.
Explanation:
When the wire is connected and then removed, the charges redistribute to minimize their potential energy. The excess charge flows from the sphere with higher potential (in this case, the positively charged sphere) to the sphere with lower potential (the negatively charged sphere). This redistribution occurs until both spheres have the same potential.
As a result, the initially positively charged sphere loses some of its charge to the initially negatively charged sphere, causing both charges to decrease. This redistribution of charges leads to a decrease in the force of repulsion between the spheres.
The new charges on the spheres can be calculated using Coulomb's law and the given force of repulsion:
0.036 = (9 x 10^9) * (q * q) / (0.5)^2
Simplifying the equation:
0.036 * 0.25 = (9 x 10^9) * (q^2)
0.009 =
Given:
Force of attraction, F = 0.108 N
Distance between the spheres, d = 0.5 m
We can use Coulomb's law to find the initial charges on the spheres.
Coulomb's law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Mathematically, it can be expressed as:
F = k * (q1 * q2) / r^2
Where:
F is the force between the charges,
k is the electrostatic constant (9 x 10^9 Nm^2/C^2),
q1 and q2 are the charges on the spheres,
r is the distance between the spheres.
Calculating the Initial Charges:
Let the charge on one sphere be q and the charge on the other sphere be -q (opposite signs).
Using the given information, we can write the equation for the force of attraction:
0.108 = (9 x 10^9) * (q * (-q)) / (0.5)^2
0.108 = (9 x 10^9) * (q^2) / 0.25
Simplifying the equation:
0.108 * 0.25 = (9 x 10^9) * (q^2)
0.027 = (9 x 10^9) * (q^2)
q^2 = 0.027 / (9 x 10^9)
q^2 = 3 x 10^(-12)
Taking the square root of both sides:
q = ± √(3 x 10^(-12))
q = ± 1.73 x 10^(-6)
Since the spheres have opposite charges, we can assign one sphere with a charge of +1.73 x 10^(-6) C and the other with a charge of -1.73 x 10^(-6) C.
Repulsion after Removing the Wire:
After connecting the spheres with a conducting wire and then removing it, the charges on the spheres redistribute. The excess charge flows from one sphere to the other until both spheres have the same potential.
Once the charges redistribute, the spheres repel each other with a force of 0.036 N, with the distance between them still being 0.5 m.
Explanation:
When the wire is connected and then removed, the charges redistribute to minimize their potential energy. The excess charge flows from the sphere with higher potential (in this case, the positively charged sphere) to the sphere with lower potential (the negatively charged sphere). This redistribution occurs until both spheres have the same potential.
As a result, the initially positively charged sphere loses some of its charge to the initially negatively charged sphere, causing both charges to decrease. This redistribution of charges leads to a decrease in the force of repulsion between the spheres.
The new charges on the spheres can be calculated using Coulomb's law and the given force of repulsion:
0.036 = (9 x 10^9) * (q * q) / (0.5)^2
Simplifying the equation:
0.036 * 0.25 = (9 x 10^9) * (q^2)
0.009 =
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Two identical conducting spheres ( of negligible radius) I having charge of of opposite sign, I attract each other with a force of 0.108 N when separated by 0.5 meter. The sphere are connected by a conducting wire which is then removed when charge stops flowing and thereafter repel each other with a force of 0.036 N keeping the distance same. I What were the initial charges on the sphere?
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Two identical conducting spheres ( of negligible radius) I having charge of of opposite sign, I attract each other with a force of 0.108 N when separated by 0.5 meter. The sphere are connected by a conducting wire which is then removed when charge stops flowing and thereafter repel each other with a force of 0.036 N keeping the distance same. I What were the initial charges on the sphere? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Two identical conducting spheres ( of negligible radius) I having charge of of opposite sign, I attract each other with a force of 0.108 N when separated by 0.5 meter. The sphere are connected by a conducting wire which is then removed when charge stops flowing and thereafter repel each other with a force of 0.036 N keeping the distance same. I What were the initial charges on the sphere? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical conducting spheres ( of negligible radius) I having charge of of opposite sign, I attract each other with a force of 0.108 N when separated by 0.5 meter. The sphere are connected by a conducting wire which is then removed when charge stops flowing and thereafter repel each other with a force of 0.036 N keeping the distance same. I What were the initial charges on the sphere?.
Two identical conducting spheres ( of negligible radius) I having charge of of opposite sign, I attract each other with a force of 0.108 N when separated by 0.5 meter. The sphere are connected by a conducting wire which is then removed when charge stops flowing and thereafter repel each other with a force of 0.036 N keeping the distance same. I What were the initial charges on the sphere? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Two identical conducting spheres ( of negligible radius) I having charge of of opposite sign, I attract each other with a force of 0.108 N when separated by 0.5 meter. The sphere are connected by a conducting wire which is then removed when charge stops flowing and thereafter repel each other with a force of 0.036 N keeping the distance same. I What were the initial charges on the sphere? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical conducting spheres ( of negligible radius) I having charge of of opposite sign, I attract each other with a force of 0.108 N when separated by 0.5 meter. The sphere are connected by a conducting wire which is then removed when charge stops flowing and thereafter repel each other with a force of 0.036 N keeping the distance same. I What were the initial charges on the sphere?.
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Two identical conducting spheres ( of negligible radius) I having charge of of opposite sign, I attract each other with a force of 0.108 N when separated by 0.5 meter. The sphere are connected by a conducting wire which is then removed when charge stops flowing and thereafter repel each other with a force of 0.036 N keeping the distance same. I What were the initial charges on the sphere?, a detailed solution for Two identical conducting spheres ( of negligible radius) I having charge of of opposite sign, I attract each other with a force of 0.108 N when separated by 0.5 meter. The sphere are connected by a conducting wire which is then removed when charge stops flowing and thereafter repel each other with a force of 0.036 N keeping the distance same. I What were the initial charges on the sphere? has been provided alongside types of Two identical conducting spheres ( of negligible radius) I having charge of of opposite sign, I attract each other with a force of 0.108 N when separated by 0.5 meter. The sphere are connected by a conducting wire which is then removed when charge stops flowing and thereafter repel each other with a force of 0.036 N keeping the distance same. I What were the initial charges on the sphere? theory, EduRev gives you an
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